Description

p₁ - inlet pressure

Absolute pressure in front of the nozzle

p₂ - throat pressure

Absolute pressure at the nozzle throat

Δp - pressure drop

Measured pressure difference

Δω - pressure loss

That can't be recovered after the nozzle

D₁ - inlet diameter

Nozzle internal inlet diameter

D₂ - throat diameter

Nozzle throat diameter

e - expansion factor

Coefficient used for compressible flow calculation

C - coefficient of discharge

Coefficient used for nozzle based on ISO 5167

R_eD - inlet Reynolds

Reynolds number calculated in front of the nozzle

R_ed - throat Reynolds

Reynolds number calculated at the nozzle throat

K - resistance coefficient

That you can use in pipeline calculation, as nozzle is creating local pressure losses in the pipeline

q₁ - volumetric flow rate

Fluid flow rate in terms of units of volume per unit of time on the inlet conditions

q - standard flow

Flow rate at standard conditions. Used only if the selected fluid is gas.

ṁ - mass flow rate

Fluid flow rate in terms of units of mass per unit of time

V₁ - upstream velocity

Flow velocity at the nozzle inlet where flow diameter is D₁

T₁ - upstream temperature

Fluid temperature for gas density calculation based on the ideal gas state equation

ρ₁ - upstream density

Fluid density at the nozzle inlet in terms of mass per unit of volume

R - gas constant

Gas constant in terms of energy per unit of mass and temperature, for gas density calculation using ideal gas state equation

κ - isentropic coefficient

Specific heat ratio

ν - kinematic viscosity

Result of fluid particles colliding to each other and moving at different velocities in terms of area per square unit of time

μ - dynamic viscosity

Result of fluid particles colliding to each other and moving at different velocities in terms of mass per square unit of distance and time

Calculation setup

Select nozzle type based on its shape

Nozzle

Classic shape

Long radius

For less pressure drop

Venturi nozzle

Shaped like Venturi

Select value to input. You should enter selected one. The other one will be calculated

p₂

pressure downstream from the nozzle

Δp

measured pressure difference in front and after the nozzle

Select value to input. You should enter selected one. The other one will be calculated

ν

kinematic viscosity

μ

dynamic viscosity

Select value to input. Available only if gas is selected. You should enter selected one. The other one will be calculated

T₁

upstream temperature.

ρ₁

upstream density.

Select fluid type

Gas

for compressible flow where ideal gas state equation is applicable

Liquid

for incompressible flow of liquids

Application of ISO 5167 constraints

ISO constraints

Deselect if you don't want to check if the nozzle and the flow conditions are within the limits of the ISO standard.

Why should you use this calculator?

Nozzles and Venturi nozzles are devices that are inserted in circular cross-section conduit to create a pressure difference of static pressure caused by the flow contraction in the throat of it. You can calculate flow rate using that pressure difference.

Due to the contraction in the diameter from the inlet to the throat of the nozzle, the flow velocity is changing while flow rate remains constant. That change in flow velocity is creating the increase of the dynamic pressure and drop of the static pressure, as total pressure remains uniform, according to the conservation law.

You can measure the change of the static pressure by measuring the pressure in the inlet and after the nozzle. That measured value is the input value for the calculation of the flow rate.

This calculator also calculates total pressure drop created by the nozzle. You can use this calculator for all three types of nozzles covered in standards: ISA 1932 nozzle, long radius nozzle, and Venturi nozzle. All three types differ from each other based on its shape. All nozzles have radius shaped convergent inlet with the cylindrical throat, and Venturi nozzle also has a divergent part as an outlet.

When is this calculator suitable?

You can use a nozzle and Venturi nozzle calculator for subsonic single-phase liquids or ideal gases. The calculator is not for pulsating flow, or non-steady flow when the flow rate is changing in time.

When is this calculator not relevant?

This calculator is not suitable for flow of multiphase fluids, like a stream of liquids that contain solid particles or stream of liquids that contain undissolved gases. Also, it is not suitable for gases that are not ideal, i.e., gases that don't relate to the perfect gas law.

Limiting factor for this calculator is when the flow reaches chocked flow and mean velocity is close to the local speed of sound. You can use gas discharge calculator for calculation of gas flow with a higher pressure drop and flow close or equal to choked flow conditions.

What else has to be known to perform the calculation?

To calculate flow rate, you have to enter the nozzle inlet and throat diameter, together with fluid properties - density and viscosity.

For a gas as flowing fluid, instead of the density, you can enter gas constant, pressure and temperature at actual conditions. Density is then calculated using an ideal gas state equation.

You should enter density on actual flow conditions, as well as real pressure and real temperature.

How is the calculation performed?

The calculator is doing calculation according to ISO 5167-3. You can expect to have accurate and reliable results solely if the device satisfies the requirements from the standard.

What are the standard ISO 5137-3 conditions?

For the flow of a perfect gas, the pressure reduction produced by the nozzle (p2/p1) must be higher than 0.75.

Limits of use for nozzles are:

50 mm < D < 500 mm
0.3 < β < 0.8
7x10⁴ < ReD < 10⁷ for 0.3 < β < 0.44
2x10⁴ < ReD < 10⁷ for 0.44 < β < 0.80

Limits of use for long radius nozzles are:

50 mm < D < 630 mm
0.2 < β < 0.8
10⁴ < ReD < 10⁷

Limits of use for Venturi nozzles are:

65 mm < D < 500 mm
0.316 < β < 0.775
1.5x10⁵ < ReD < 2x10⁶

What happens if a calculation is not within these limits?

If the nozzle characteristics or flow conditions are not according to the ISO 5167-3 calculator presents the warning message. If you still want to perform calculation regardless of the states in the standard, you can choose not to use ISO constraints in the computation.